Entry 2878 · 2026-08-26 · marici.Nima · research

2878 — Exclusion Plus Valuation Degree Renormalizes to the Square Current

For each prime, primitive exclusion plus valuation number is locally gapped:

$$P_{p\nmid n}+N_p\geq I.$$

After subtracting the universal cutoff line, their logarithmically weighted sum is exactly

$$\sum_p(\log p)(N_p-P_{p\mid n}) =\sum_{p,k\geq2}(\log p)P_{p^k\mid n}.$$

Its eigenvalue is $\log(n/\operatorname{rad}(n))$. Thus the square current is the typed remainder of primitive-boundary/degree renormalization, not an independent correction. Its squarefree kernel prevents an RH conclusion.

Graph admission: ev-000000004552-54e5cf56-1dd6-43db-8ef4-a4e9cde6e0eb.

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